for \(q\) , \(r > 0\) .
For example, if we want our gradient method to have shorter steps more often than long ones, we may keep \(r = 1\)  but select a higher value of \(q\) , e.g., \(q = 2\) . This mimics the effect of setting \(\eta \)  relatively close to 1, as it is done in [1]}.
The following result ensures that this “cotangent step” (REF ) indeed may be regarded as a continuous extension of the ABB step, having similar properties for \(\angle (\mathbf {s}, \mathbf {y})\)  close to 0 or \(\pi /2\) .
